Discrete orthogonal ensemble on the exponential lattices

2022/06/17 by Forrester, Peter J, Li, Shi-Hao, Shen, Bo-Jian +1 · 1 citation
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2206.08633

Abstract

Inspired by Aomoto's q-Selberg integral, the orthogonal ensemble in the exponential lattice is considered in this paper. By introducing a skew symmetric kernel, the configuration space of this ensemble is constructed to be symmetric and thus, corresponding skew inner product, skew orthogonal polynomials as well as correlation functions are explicitly formulated. Examples including Al-Salam & Carlitz, q-Laguerre, little q-Jacobi and big q-Jacobi cases are considered.

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• Spectral analysis of q-deformed unitary ensembles with the Al-Salam--Carlitz weight

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